You can check it by the fact that momentum conservation has to be sadisfied. For example. A photon with energy E=2mc^2 where m is the mass of the electron is coming. It can create a pair with its energy. But then there is no energy left, thus the electron and positron have no kinetic energy and thus no momentum. But the photon had momentum (-> momentum conservation not sadisfied). There must be a nucleon that takes a short amaount of energy from the photon. Given the fact that a nucleon has a very high mass momentun conservation can be sadisfied.

You understand?

And the relation you can calculate with momentum and energy as above is given by Einsteins energy momentum relation:
E^2=(pc)^2+m^2c^4. One can show that this equation obeys special relativity.

It is possible to have pair production in the absence of a nucleus. To do this you need two photons colliding. This was the situation immediately after the big bang. That's how matter was produced. It is still not completely settled as to why there was some matter left over.

Perception-wise, pair-production is an energy dependent extension of the photo-electric phenomenon; As the photon energy approaches 1 MeV the probability for emission of a single electron decreases toward zero. At about a photon energy of 1.022 MeV the probability for pair-production inreases from zero with increasing photon energy. Cheers. Jim

To answer EL. Photon-photon collisions lead to the production of matter-antimatter pairs. Matter-antimatter collsions destroy both particles. Somehow or other antimatter particles independently disappeared and matter particles were left. The open question concerns the exact mechanisms for this process.

Mathman. My objection was that to me it sounded like you were saying that after the Big Bang the universe was consisting of photons, which in there turn produced the matter-antimatter.
Why wouldn't it be the other way around?
The matter-antimatter assymetry could have been there "from the start", and need not have anything to do with matter-antimatter pair creation out of photons.

All descriptions of the big bang that I have seen indicate that it started with pure energy. The problem of the excess of matter is an important open question.

Recall that "pure energy" is a physically meaningless concept. All energy is stored in one form or another. If you have a gas of photons the energy is in the kinetic energy of the photons. If you have a gas of massive particles, some of the energy is in the mass of the particles, and the rest is in the kinetic energy. If the particles have charges then there are potential energies and so on, it can get quite complicated, but no form of energy is more "pure" than any other.

What form the energy of the big bang started in, we don't know. We do know that, if inflation is correct, the energy of everything we see around us today was initially stored in the so-called inflaton field. At the end of inflation, the inflaton decayed into Standard Model particles (a process called reheating). We don't know the details of this decay, but a good guess is that it went roughly equally into all Standard Model particles. To make contact with the earlier part of this thread, two photon scattering would then be important to bring this mixture into thermal equilibrium.

(Of course, as was said before, none of this addresses the problem of why there is more matter than anti-matter).

All descriptions of the big bang that I have seen indicate that it started with pure energy.

What is then pure energy? I think Ben Lillie summarized the topic well.
All I wanted to say is that the process of pair production through photon collisions does not have to have anything to do with the asymmetry problem, although it of course could. We just don't know at present time.

To clarify: What I intended to mean by "pure energy" is that at the big bang creation there were no leptons or quarks, but only photons. I may have oversimplified, but there is no theory that I have seen which implies that the matter excess was there from the creation. The problem of matter existence (excess over antimatter) is a major current question.

1) Was there an asymmetry in matter vs. antimatter in the initial conditions of the universe?

2) How was the energy at that time distributed among the available degrees of freedom?

If inflation is correct, the answer to the first question is actually "it doesn't matter". The reason is that once the universe begins inflating the matter asymmetry is dynamically set to zero. This is the reason that identifying the mechanism to generate the asymmetry is a problem. Prior to the theory of inflation, people just assumed that the matter asymmetry was set by initial conditions.

The answer to number 2 obviously depends on when exactly we're talking about. However, at no time was all the energy in photons. The early universe after inflation (which is as close as we can meaningfully come to the beginning) was a system in thermal equilibrium. Early on the temperature of the universe was high enough that Standard Model particles were massless. Statistical mechanics arguments then show that the energy was equally divided between all available degrees of freedom. This includes the quark and lepton fields (as well as the gluons, W, Z, and Higgs), but with equal ammounts in anti-quark and anti-lepton fields, so there was no net matter.

To clarify: What I intended to mean by "pure energy" is that at the big bang creation there were no leptons or quarks, but only photons.

And this is where I think you are wrong. As BenLillie again nicely explained the early universe was probably in thermal equilibrium, which at high temperature means that the energy was equally divided between all kinds of particles (or really between all degrees of freedom).
Where have did you get that the early universe only consisted of photons from?

It is now a question of exact time. We really don't know what was the state at time t=0. The equilibrium you are talking about is immediately afterwards, maybe t=10-43 sec. In any case, the point I was trying to make is that there is nothing in any theory I have seen which indicates an excess of matter over antimatter at the beginning. CP violation is supposed to account for the current existence of matter, but a quantitative description has yet to be made.

It is now a question of exact time. We really don't know what was the state at time t=0. The equilibrium you are talking about is immediately afterwards, maybe t=10-43 sec. In any case, the point I was trying to make is that there is nothing in any theory I have seen which indicates an excess of matter over antimatter at the beginning. CP violation is supposed to account for the current existence of matter, but a quantitative description has yet to be made.

Yes I agree. I only mensioned initial asymmetry as an option.
It was your statement that the matter was produced through photon-photon collisions I didn't like:

It is possible to have pair production in the absence of a nucleus. To do this you need two photons colliding. This was the situation immediately after the big bang. That's how matter was produced. It is still not completely settled as to why there was some matter left over.

It was your statement that the matter was produced through photon-photon collisions I didn't like:

Why don't you like it? This is simply the inverse reaction to the matter-antimatter reaction which leads to a pair of photons. As I said, it the photon-photon collision produces a matter-antimatter pair and the question (as I have already said) is how did we get an excess of matter?

I don't know if we are just talking beside each other, but I get the impression you are saying this:

First there was the Big Bang.
After the Big Bang the universe consisted of photons only.
The rest of the matter was created through photon-photon collisions.

Why I have gotten this impression is because you wrote

This was the situation immediately after the big bang. That's how matter was produced. It is still not completely settled as to why there was some matter left over

and

What I intended to mean by "pure energy" is that at the big bang creation there were no leptons or quarks, but only photons.

If I have interpreted you correctly, then I have to ask you: Why would the universe consist only out of photons after the Big Bang? Why not only out of electrons, or only out of Higgs bosons? What makes photons so special you think only they were there from the start?

As mensioned earlier the standard picture of the matter content after the Big Bang is an equal distribution between all degrees of freedom (all different particles), since at such high temperature all particles can be seen as massless.